I haven't posted any math's because it's just common sense and I'm too lazy. So let's review shall we..........run of 10 is 1024-1 according to wizard of odds
very rare occurrence, my opinion is the odds of seeing the same sequence soon after is even rarer my opinion is that if you do see it then the odds of seeing 2 huge runs back to back again is even rarer still .....it's happened and not likely to repeat any time soon. Your argument is it's random and it will repeat. Odd's my friend is all it is. In layman's terms it could happen but it probably won't.
Rouletteguy,
The mistake you are making is the schoolbook example of the gamblers fallacy. It is a combination of two misconceptions, misunderstandings that together typically lead to a monetary loss that is inversely proportional to the time it takes one to realize these mistakes.
I'll try to explain these in layman's terms. For our sample lets use a roulette without 0 so that the red/black odds are exactly 1/2. Consider the following three sequences of 10 spins :
Sequence A : red red red red red red red red red red
Sequence B : black black red black red black red red red black
Sequence C : red black black red black red red black red black
From the wizard of odds you've learned that the odds for sequence A are 1 in 1024. Do you fully appreciate that the odds for sequence B are also 1 in 1024 ? And the same for sequence C ?
The first mistake, in layman's terms, is to try and detect patterns. A gambler that suffers from the gamblers fallacy will judge sequence A as being less likely than sequence B or C - because his brains pattern detector doesn't trigger on sequence B or C, and so he fails to differentiate between the two, resulting in the (wrong) perception that B and C are the same type of events (those without pattern) which to him feel more common than sequence A.
Since the collection of all runs in which you don't detect a pattern is much larger than the collection of all runs in which you do detect a pattern, you end up with the belief that somehow a run of 10 reds like in sequence A is less likely to occur than sequence B or C.
Detecting patterns in a random event is like searching for figures in the clouds - it can be very fun - but they're not really there.
The second mistake is in essence the gamblers fallacy itself but it is important to realize that you can only make it after you make the first mistake. It is the belief that red after sequence A is less likely to occur
than red after sequence B or C. From a mathematical point of view the odds of seeing sequence A, B or C followed by red are all 1 in 2048.
So, to recap :
mistake 1 : looking for patterns.
mistake 2 : assuming a random distribution averages out on the short or mid term.
But mistake 1 is by far the most important one here. A random sequence is the never-ending mix of all possible patterns. In fact, one of the best ways to prove an event is not random is by finding a pattern that doesn't occur.
To close, consider the following analogy .. looking for patterns in random data is like shooting blindfolded at a wall, then going in to paint bull's eyes around the bullet holes. If you do the shooting before the painting - its not target practice. If you didn't predict it - its not a pattern.
Cheers,
Enzo